Related papers: Polymer models with competing collapse interaction…
We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice of general coordination $q$ and on a Husimi lattice built with squares and coordination $q=4$. The exact grand-canonical solutions of the model are obtained,…
We study by computer simulation a recently introduced generalised model of self-interacting self-avoiding trails on the square lattice that distinguishes two topologically different types of self-interaction: namely crossings where the…
We obtain the solution of models of self-avoiding walks with attractive interactions on Husimi lattices built with squares. Two attractive interactions are considered: between monomers on first-neighbor sites and not consecutive along a…
There have been separate studies of the polymer collapse transition, where the collapse was induced by two different types of attraction. In each case, the configurations of the polymer were given by the same subset of random walks being…
Various interacting lattice path models of polymer collapse in two dimensions demonstrate different critical behaviours. This difference has been without a clear explanation. The collapse transition has been variously seen to be in the…
The exact grand-canonical solution of a generalized interacting self-avoid walk (ISAW) model, placed on a Husimi lattice built with squares, is presented. In this model, beyond the traditional interaction $\omega_1=e^{\epsilon_1/k_B T}$…
We solve a model of self-avoiding walks with up to two monomers per site on the Bethe lattice. This model, inspired on the Domb-Joyce model, was recently proposed to describe the collapse transition observed in interacting polymers [J.…
We study the localisation of lattice polymer models near a permeable interface in two dimensions. Localisation can arise due to an interaction between the polymer and the interface, and can be altered by a preference for the bulk solvent on…
In earlier work we provided the first evidence that the collapse, or coil-globule, transition of an isolated polymer in solution can be seen in a four-dimensional model. Here we investigate, via Monte Carlo simulations, the canonical…
We propose and study a model of polymer chains in a bilayer. Each chain is confined in one of the layers and polymer bonds on first neighbor edges in different layers interact. We also define and comment results for a model with…
Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently, a two-dimensional model (triangular…
The study of the effect of random impurities on the collapse of a flexible polymer in dilute solution has had recent attention with consideration of semi-stiff interacting self-avoiding walks on the square lattice. In the absence of…
We investigate polymers pulled away from an interacting surface, where the force is applied to the untethered endpoint and at an angle $\theta$ to the surface. We use the canonical self-avoiding walk model of polymers and obtain the phase…
A generalised model for interacting self-avoiding trails on the square lattice is presented and studied using numerical transfer matrix methods. The model differentiates between on-site double visits corresponding to collisions, and…
We solve a model of polymers represented by self-avoiding walks on a lattice which may visit the same site up to three times in the grand-canonical formalism on the Bethe lattice. This may be a model for the collapse transition of polymers…
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model…
We investigate a lattice model of polymers where the nearest-neighbour monomer-monomer interaction strengths differ according to whether the local configurations have so-called ``hydrogen-like'' formations or not. If the interaction…
We study a model of semi-flexible self-avoiding trails, where the lattice paths are constrained to visit each lattice edge at most once, with configurations weighted by the number of collisions, crossings and bends, on a Husimi lattice…
We introduce a new class of models for polymer collapse, given by random walks on regular lattices which are weighted according to multiple site visits. A Boltzmann weight $\omega_l$ is assigned to each $(l+1)$-fold visited lattice site,…
A two-dimensional square-lattice model for the formation of secondary structures in proteins, the hydrogen-bonding model, is extended to include the effects of solvent quality. This is achieved by allowing configuration-dependent…